No. It's not possible to guess someone else's article (I guess you probably mean reading records here). Those reading records must be get or set with a cookie that indicate the user has logged in with the right account (which is done by ajax in the code).
It looks to me that the url that calls queries_read_records.like_article() only requires a logged in user and a record id in order to set a read record as liked? Are you saying that is not possible to guess the id because it's not a sequential number by default in mongodb?
The article id is public (they are public on the Internet anyway). But it's not possible (at least as designed) to access any user-specific information if not logged in.
I'm really surprised that so many people are still just talking about it in an economic prospective. I'm not talking about Human Rights or Freedom because the government don't event accept them. I just want to surf the Internet.
Currently it works well because we get more and more tools to deal with GFW, but do you know how frustrating it is in the early days of the Internet in China that you spent nearly half of your life just to solve "networking issues"?
Put yourself in others' shoes for a moment please.